public void SparseSquareMatrixAgreement()
{
int d = 6;
SparseSquareMatrix A = new SparseSquareMatrix(d);
SquareMatrix B = new SquareMatrix(d);
Random rng = new Random(1);
for (int i = 0; i < 2 * d; i++)
{
int r = (int)Math.Floor(rng.NextDouble() * d);
int c = (int)Math.Floor(rng.NextDouble() * d);
A[r, c] = 2.0 * rng.NextDouble() - 1.0;
B[r, c] = A[r, c];
}
RowVector u = new RowVector(d);
ColumnVector v = new ColumnVector(d);
for (int i = 0; i < d; i++)
{
u[i] = 2.0 * rng.NextDouble() - 1.0;
v[i] = 2.0 * rng.NextDouble() - 1.0;
}
RowVector uA = u * A;
RowVector uB = u * B;
Assert.IsTrue(TestUtilities.IsNearlyEqual(uA, uB));
ColumnVector Av = A * v;
ColumnVector Bv = B * v;
Assert.IsTrue(TestUtilities.IsNearlyEqual(Av, Bv));
}
public void ExtendedVectorNorm()
{
// Check that vector norm is correctly computed even when vector is enormous (square would overflow) or tiny (square woudl underflow)
double x = Double.MaxValue / 32.0;
// Use the pythagorian quadrouple (2, 3, 6, 7)
ColumnVector v = new ColumnVector(2.0, 3.0, 6.0);
Assert.IsTrue(TestUtilities.IsNearlyEqual(v.Norm(), 7.0));
ColumnVector bv = x * v;
Assert.IsTrue(TestUtilities.IsNearlyEqual(bv.Norm(), 7.0 * x));
ColumnVector sv = v / x;
Assert.IsTrue(TestUtilities.IsNearlyEqual(sv.Norm(), 7.0 / x));
// Use the pythagorian 7-tuple (1, 2, 3, 4, 5, 27, 28)
RowVector u = new RowVector(1.0, 2.0, 3.0, 4.0, 5.0, 27.0);
Assert.IsTrue(TestUtilities.IsNearlyEqual(u.Norm(), 28.0));
RowVector bu = x * u;
Assert.IsTrue(TestUtilities.IsNearlyEqual(bu.Norm(), 28.0 * x));
RowVector su = u / x;
Assert.IsTrue(TestUtilities.IsNearlyEqual(su.Norm(), 28.0 / x));
}
public void Test_RowVector_Operator()
{
RowVector l = new RowVector(1, 1, 1);
RowVector r = new RowVector(1, 1, 1);
RowVector add = l + r;
Assert.True(RowVector.Equals(add, new RowVector(2, 2, 2), Ep));
RowVector sub = l - r;
Assert.True(RowVector.Equals(sub, new RowVector(0, 0, 0), Ep));
RowVector mul = l * 2;
Assert.True(RowVector.Equals(mul, new RowVector(2, 2, 2), Ep));
RowVector mur = 2 * r;
Assert.True(RowVector.Equals(mur, new RowVector(2, 2, 2), Ep));
RowVector div = l / 2;
Assert.True(RowVector.Equals(div, new RowVector(0.5, 0.5, 0.5), Ep));
}
/// <summary>
/// Return row of a matrix
/// </summary>
/// <param name="rowIndex"></param>
/// <returns>Vector</returns>
public static RowVector GetAugmentedRow(this RealMatrix matrix, int rowIndex)
{
var row = matrix.B[rowIndex].GetRange(0, matrix.AugmentedColumnCount).ToList();
var vector = new RowVector(v: row);
return(vector);
}
/// <summary>
/// Replace row with vector that same size
/// </summary>
/// <param name="vector">Vector</param>
/// <param name="rowIndex">Row index</param>
public static void WriteOnRow(this RealMatrix matrix, RowVector rowVector, int rowIndex, bool isAugmentedRow = false)
{
//check that matrix row length (column count) is equal to vector length
//and row index is valid
if (!isAugmentedRow)
{
if (rowVector.V.Count != matrix.ColumnCount && rowIndex >= matrix.RowCount)
{
return;
}
for (int i = 0; i < rowVector.V.Count; i++)
{
matrix.M[rowIndex][i] = rowVector.V[i];
}
}
else
{
if (rowVector.V.Count != matrix.AugmentedColumnCount && rowIndex >= matrix.AugmentedRowCount)
{
return;
}
for (int i = 0; i < rowVector.V.Count; i++)
{
matrix.B[rowIndex][i] = rowVector.V[i];
}
}
matrix.MatrixElementsChanged();
}
/// <summary>
/// Sets the r'th row of the matrix m to x.
/// Requires: x.Dimension == m.ColumnCount
/// </summary>
/// <param name="m">A matrix whose r'th row will be modified.</param>
/// <param name="x">A row vector to copy into m.</param>
/// <param name="r">The zero-based index of the row of m to be modified.</param>
public static void CopyRowInto(this RectangularMatrix m, RowVector x, int r)
{
for (int i = 0; i < x.Dimension; ++i)
{
m[r, i] = x[i];
}
}
public void RowVectorArithmetic()
{
// addition and multiplication by a double
RowVector RA = R + R;
RowVector R2 = 2.0 * R;
Assert.IsTrue(RA == R2);
// subtraction and multiplication by a double
RowVector RS = R - R;
RowVector R0 = 0.0 * R;
Assert.IsTrue(RS == R0);
// negation and multiplication by -1
RowVector RN = -R;
RowVector RD = R / (-1.0);
Assert.IsTrue(RN == RD);
// multiply a column by a matrix
RowVector RM = R * M;
Assert.IsTrue(RM.Dimension == M.ColumnCount);
// dot multiply
ColumnVector RT = R.Transpose();
double dot = R * RT;
Assert.IsTrue(dot > 0);
}
public void ColumnVectorArithmetic()
{
// addition and multiplication by a double
ColumnVector CA = C + C;
ColumnVector C2 = 2.0 * C;
Assert.IsTrue(CA == C2);
// subtraction and multiplication by a double
ColumnVector CS = C - C;
ColumnVector C0 = 0.0 * C;
Assert.IsTrue(CS == C0);
// negation and division by -1
ColumnVector CN = -C;
ColumnVector CD = C / (-1.0);
Assert.IsTrue(CN == CD);
// multiply a column by a matrix
ColumnVector MC = M * C;
Assert.IsTrue(MC.Dimension == M.RowCount);
// dot multiply
RowVector CT = C.Transpose();
double dot = CT * C;
Assert.IsTrue(dot > 0);
}
public void UnitMatrixArithmetic()
{
SquareMatrix A = new SquareMatrix(new double[, ] {
{ 1.0, -2.0 },
{ -3.0, 4.0 }
});
SquareMatrix AI = A * UnitMatrix.OfDimension(A.Dimension);
Assert.IsTrue(A == AI);
SquareMatrix IA = UnitMatrix.OfDimension(A.Dimension) * A;
Assert.IsTrue(IA == A);
ColumnVector c = new ColumnVector(1.0, 2.0, 3.0);
ColumnVector Ic = UnitMatrix.OfDimension(c.Dimension) * c;
Assert.IsTrue(Ic == c);
RowVector r = new RowVector(0.0, 1.0);
RowVector rI = r * UnitMatrix.OfDimension(r.Dimension);
Assert.IsTrue(rI == r);
Assert.IsTrue(UnitMatrix.OfDimension(A.Dimension) == UnitMatrix.OfDimension(A.Dimension));
Assert.IsTrue(0.0 * UnitMatrix.OfDimension(3) == UnitMatrix.OfDimension(3) - UnitMatrix.OfDimension(3));
Assert.IsTrue(1.0 * UnitMatrix.OfDimension(3) == UnitMatrix.OfDimension(3));
Assert.IsTrue(2.0 * UnitMatrix.OfDimension(3) == UnitMatrix.OfDimension(3) + UnitMatrix.OfDimension(3));
}
public void MultiplicationRowVectorByColumnVectorExceptionTest()
{
var v1 = new RowVector(new double[] { 1, 2, 3, 4 });
var v2 = new ColumnVector(new double[] { 5, 6, 7, 8, 9 });
var scalarProduct = v1 * v2;
}
public void ScalarProductExceptionTest()
{
var v1 = new RowVector(new double[] { 1, 2, 3, 4 });
var v2 = new RowVector(new double[] { 5, 6, 7, 8, 9 });
var scalarProduct = v1 * v2;
}
/// <summary>
/// Return row of a matrix
/// </summary>
/// <param name="rowIndex"></param>
/// <returns>Vector</returns>
public static RowVector GetRow(this RealMatrix matrix, int rowIndex)
{
var row = new List <IR.RealNumber>();
row.AddRange(matrix.M[rowIndex].GetRange(0, matrix.ColumnCount).ToList());
var vector = new RowVector(v: row);
return(vector);
}
/// <summary>
/// Computes the profit-maximizing decision (DECT0), given true costs and selling prices.
/// </summary>
/// <returns>A [1 x ip.CO] vector of 1's and 0's. 1.0 (0.0) indicates
/// that the product is (not)included in the profit-maximizing product mix.</returns>
public RowVector CalcOptimalDecision()
{
RowVector pc_b = CalcTrueProductCosts();
RowVector productProfits = this.sp - pc_b;
// Replace each negative (nonnegative) element of productProfits with a 0.0 (1.0)
var dect0 = productProfits.Map(x => ((x < 0.0) ? 0.0 : 1.0));
return(new RowVector(dect0));
}
public void VectorNorm()
{
RowVector nR = R / R.Norm();
Assert.IsTrue(TestUtilities.IsNearlyEqual(nR.Norm(), 1.0));
ColumnVector nC = C / C.Norm();
Assert.IsTrue(TestUtilities.IsNearlyEqual(nC.Norm(), 1.0));
}
public void InstantiateRowVectorWithArray()
{
var vector = new RowVector(new double[] { 1, 2, 3, 4 });
var expectedValues = new double[] { 1, 2, 3, 4 };
bool isEqual = Helpers.AreEqualVector(expectedValues, vector);
Assert.IsTrue(isEqual);
}
public void InstantiateRowVectorWithValueTest()
{
var vector = new RowVector(4);
var expectedValues = new double[] { 0, 0, 0, 0 };
bool isEqual = Helpers.AreEqualVector(expectedValues, vector);
Assert.IsTrue(isEqual);
}
public void InstantiateColumnVectorWithVector()
{
var v = new RowVector(new double[] { 1, 2, 3, 4 }) as Vector;
var vector = new ColumnVector(v);
var expectedValues = new double[] { 1, 2, 3, 4 };
bool isEqual = Helpers.AreEqualVector(expectedValues, vector);
Assert.IsTrue(isEqual);
}
public void MultiplicationRowVectorByColumnVectorTest()
{
var v1 = new RowVector(new double[] { 1, 2, 3, 4 });
var v2 = new ColumnVector(new double[] { 5, 6, 7, 8 });
var expectedResult = 70;
var scalarProduct = v1 * v2;
Assert.AreEqual(expectedResult, scalarProduct);
}
public void ScalarProductTest()
{
var v1 = new RowVector(new double[] { 1, 2, 3, 4 });
var v2 = new RowVector(new double[] { 5, 6, 7, 8 });
var expectedScalarProduct = 70;
var scalarProduct = v1 * v2;
Assert.AreEqual(expectedScalarProduct, scalarProduct);
}
public void RectangularMatrixAccess()
{
// create a matrix via outer product
ColumnVector cv = new ColumnVector(new double[] { 1, 2 });
RowVector rv = new RowVector(new double[] { 3, 4, 5 });
RectangularMatrix M = cv * rv;
// check dimensions
Assert.IsTrue(M.RowCount == cv.Dimension);
Assert.IsTrue(M.ColumnCount == rv.Dimension);
// check values
for (int r = 0; r < M.RowCount; r++)
{
for (int c = 0; c < M.ColumnCount; c++)
{
Assert.IsTrue(M[r, c] == cv[r] * rv[c]);
}
}
// extract a column
ColumnVector mc = M.Column(1);
Assert.IsTrue(mc.Dimension == M.RowCount);
for (int i = 0; i < mc.Dimension; i++)
{
Assert.IsTrue(mc[i] == M[i, 1]);
}
// extract a row
RowVector mr = M.Row(1);
Assert.IsTrue(mr.Dimension == M.ColumnCount);
for (int i = 0; i < mr.Dimension; i++)
{
Assert.IsTrue(mr[i] == M[1, i]);
}
// test clone
RectangularMatrix MC = M.Copy();
Assert.IsTrue(MC.RowCount == M.RowCount);
Assert.IsTrue(MC.ColumnCount == M.ColumnCount);
// test equality of clone
Assert.IsTrue(MC == M);
Assert.IsFalse(MC != M);
// test independence of clone
MC[0, 0] += 1.0;
Assert.IsFalse(MC == M);
Assert.IsTrue(MC != M);
}
/// <summary>
/// Computes the profit-maximizing production quantities (QT), given true costs and selling prices.
/// </summary>
/// <returns>A [ip.CO x 1] vector of production quantities.</returns>
public ColumnVector CalcOptimalVol()
{
RowVector dect0 = CalcOptimalDecision();
if (mxq.Dimension != dect0.Dimension)
{
throw new ApplicationException("MXQ and DECT0 have different lengths.");
}
var qt = mxq.Zip(dect0, (maxq, decision) => maxq * decision);
return(new ColumnVector(qt.ToArray()));
}
public void TransposeTest()
{
var rowVector = new RowVector(new double[] { 1, 2, 3, 4 });
var columnVector = rowVector.Transpose();
var expectedColumnVector = new double[] { 1, 2, 3, 4 };
Assert.IsInstanceOfType(columnVector, typeof(ColumnVector));
bool isEqual = Helpers.AreEqualVector(expectedColumnVector, columnVector);
Assert.IsTrue(isEqual);
}
public static void VectorsAndMatrices()
{
ColumnVector v = new ColumnVector(0.0, 1.0, 2.0);
ColumnVector w = new ColumnVector(new double[] { 1.0, -0.5, 1.5 });
SquareMatrix A = new SquareMatrix(new double[, ] {
{ 1, -2, 3 },
{ 2, -5, 12 },
{ 0, 2, -10 }
});
RowVector u = new RowVector(4);
for (int i = 0; i < u.Dimension; i++)
{
u[i] = i;
}
Random rng = new Random(1);
RectangularMatrix B = new RectangularMatrix(4, 3);
for (int r = 0; r < B.RowCount; r++)
{
for (int c = 0; c < B.ColumnCount; c++)
{
B[r, c] = rng.NextDouble();
}
}
SquareMatrix AI = A.Inverse();
PrintMatrix("A * AI", A * AI);
PrintMatrix("v + 2.0 * w", v + 2.0 * w);
PrintMatrix("Av", A * v);
PrintMatrix("B A", B * A);
PrintMatrix("v^T", v.Transpose);
PrintMatrix("B^T", B.Transpose);
Console.WriteLine($"|v| = {v.Norm()}");
Console.WriteLine($"sqrt(v^T v) = {Math.Sqrt(v.Transpose * v)}");
UnitMatrix I = UnitMatrix.OfDimension(3);
PrintMatrix("IA", I * A);
Console.WriteLine(v == w);
Console.WriteLine(I * A == A);
}
private void Populate(List <TrainingSetRecord> datalist)
{
for (int i = 0; i < datalist.Count; i++)
{
RowVector row = new RowVector((double)DataCell[0].Values.Where(v => v.Value == datalist[i].Tempo.ToString()).FirstOrDefault().Key
, (double)DataCell[1].Values.Where(v => v.Value == datalist[i].Danceability.ToString()).FirstOrDefault().Key
, (double)DataCell[2].Values.Where(v => v.Value == datalist[i].Energy.ToString()).FirstOrDefault().Key
, (double)DataCell[3].Values.Where(v => v.Value == datalist[i].Key.ToString()).FirstOrDefault().Key);
Dataset.AddRow(row);
Target.AddRow(new RowVector(datalist[i].Grouping.ToList()[0].Favourite.Value ? 1f : 0f));
}
}
public void VectorAsMatrix()
{
RowVector r = new RowVector(1.0, 2.0, 3.0);
Assert.IsTrue(r[0, 1] == r[1]);
r[0, 1] = 0.0;
Assert.IsTrue(r[1] == 0.0);
ColumnVector c = r.Transpose.Copy();
Assert.IsTrue(c[1, 0] == 0.0);
c[1, 0] = 2.0;
Assert.IsTrue(c[1] == 2.0);
}
internal RowVector GetVector()
{
var vector = new RowVector(this.RowQuantity * this.ColumnQuantity);
for (var idxRow = 0; idxRow < this.RowQuantity; idxRow++)
{
for (var idxCol = 0; idxCol < this.ColumnQuantity; idxCol++)
{
vector[(idxRow * this.ColumnQuantity) + idxCol] = this[idxRow, idxCol];
}
}
return(vector);
}
public void RowVectorCopy()
{
RowVector v = new RowVector(3);
// test cloning and equality/inequality testing
RowVector vc = v.Copy();
Assert.IsTrue(vc == v);
Assert.IsFalse(vc != v);
// test independence clone and equality/inequality testing
vc[0] += 1.0;
Assert.IsFalse(vc == v);
Assert.IsTrue(vc != v);
}
public void MultiplyVectorByMatrixTest()
{
var m = new Matrix(new double[, ] {
{ 1, 2, 3, 4 }, { 5, 6, 7, 8 }, { 9, 10, 11, 12 }
}, true);
var v = new RowVector(new double[] { 1, 2, 3 });
var expectedVector = new RowVector(new double[] { 38, 44, 50, 56 });
var resVector = v * m;
var isEqual = Helpers.AreEqualVector(expectedVector, resVector);
Assert.IsTrue(isEqual);
}
public void Test09()
{
RowVector rv = new RowVector(1, 2, 3);
ColumnVector cv = new ColumnVector(1, 2, 3);
double val = rv * cv;
Assert.AreEqual(14, val, LisysConfig.CalculationLowerLimit);
Matrix m = cv * rv;
Assert.AreEqual(new Matrix(new double[, ] {
{ 1, 2, 3 }, { 2, 4, 6 }, { 3, 6, 9 }
}), m);
}
public void Test_Combination()
{
RowVector rv = new RowVector(1, 2, 3);
ColumnVector cv = new ColumnVector(1, 2, 3);
Assert.That(rv * cv, Is.EqualTo(14).Within(Ep));
Assert.That(cv * rv, Is.EqualTo(
new Matrix(new [, ] {
{ 1.0, 2, 3 },
{ 2, 4, 6 },
{ 3, 6, 9 }
})
).Within(Ep)
);
}